
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
Let $\{a_n\}$ be a geometric sequence and $\{b_n\}$ be an arithmetic sequence with $b_1 = 0$. Define $\{c_n\} = \{a_n + b_n\}$, and suppose that $\{c_n\}$ is the sequence 1, 1, 2, .... Find the sum of the first 10 terms of $\{c_n\}$.

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