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Inclusion Criteria:

* Histological or cytological confirmation of a solid, malignant tumour that is refractory to standard therapies or for which no standard therapies exist
* For Cohort 3-1 and 3-2, followed as, Histological or cytological confirmation of a solid, malignant tumour that is refractory to standard therapies or for which no standard therapies exist or where treatment with paclitaxel is an appropriate treatment option. SqNSCLC patients are excluded from the Cohort 3-2.
* World Health Organisation (WHO) performance status (PS) 0-1 with no deterioration over the previous 2 weeks prior to informed consent and minimum life expectancy of 12 weeks
* At least one lesion that can be accurately assessed at baseline by computed tomography (CT) magnetic resonance imaging (MRI) or plain X-ray and is suitable for repeated assessment

Exclusion Criteria

* Prior chemotherapy, biological therapy, radiation therapy, antiandrogens, other anticancer therapies including immunotherapy and any investigational agents within 21 days of starting study treatment (not including palliative radiotherapy at focal sites), or corticosteroids within 14 days of starting study treatment.
* Major surgery within 4 weeks prior to the study treatment (excluding placement of vascular access), or minor surgery within 2 weeks prior to the study treatment
* Potent or moderate inhibitors or inducers of cytochrome (CYP) 3A4/5 if taken within the stated washout periods:
* Potent or moderate inhibitors or inducers of CYP2C8 if taken within the stated washout periods:
* Exposure to sensitive or narrow therapeutic range substrates of the drug metabolising enzymes CYP2C8, CYP2C9, CYP2C19, CYP2D6 or the drug transporters P-gp (MDR1), Breast cancer resistance protein (BCRP), Organic anion transporting polypeptide (OATP)1B1, OATP1B3, Organic cation transporter (OCT)1 and OCT2 within the appropriate wash-out period (at least 5 x reported terminal elimination half-life (t1/2) of each drug) before the study treatment.
* Any haemopoietic growth factors (eg, granulocyte-colony stimulating factor \[G-CSF\]) within 2 weeks prior to receiving study drug
* Previous initiation of treatment with AZD2014 in the present study or prior treatment with AZD8055
* With the exception of alopecia, any unresolved toxicities from prior chemotherapy greater than Common toxicity criteria for adverse events (CTCAE) grade 1 at the time of starting study treatment
* Spinal cord or brain metastases unless asymptomatic and stable off steroids for at least 4 weeks prior to start of study treatment
* Subjects with interstitial lung disease as a complication or a history

• Chūōku, Japan
• Kashiwa, Japan