
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
The sequence $\{a_n\}$ is a geometric sequence with the first term $a$ and common ratio $q$. The sequence $\{b_n\}$ satisfies $b_n=1+a_1+a_2+\ldots+a_n \ (n=1,2,\ldots)$, and the sequence $\{c_n\}$ satisfies $c_n=2+b_1+b_2+\ldots+b_n \ (n=1,2,\ldots)$. If $\{c_n\}$ is a geometric sequence, calculate $a+q$.

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