
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given the arithmetic sequence $\{a_{n}\}$ where $a_{1}=3$, and $a_{2}+a_{5}=11$.
(I) Find the general term formula $a_{n}$ for the sequence;
(II) If $c_{n}=2^{a_{n}-2}+n$, find the sum of the first 10 terms $S_{10}$ for the sequence $\{c_{n}\}$.

Present the answer in LaTex format: \boxed{Your answer}
user