
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 that the sequence $\{a_n\}$ is an arithmetic sequence with a first term of 1 and $\{b_n\}$ is a geometric sequence, let $c_n = a_n + b_n$, and the first three terms of the sequence $\{c_n\}$ are 3, 6, and 11.
(1) Find the general formulas for sequences $\{a_n\}$ and $\{b_n\}$.
(2) Find the sum of the first 10 terms, $S_{10}$, of the sequence $\{c_n\}$.

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