
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 $S_n$ be the sum of the first $n$ terms of $\{a_n\}$. For any positive integer $n$, it holds that $a_n + 2a_{n+1} + a_{n+2} = 0$. Given that $a_1 = 2$, calculate the value of $S_{101}$.

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