
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 a sequence $\{a_n\}$ where for all $n \in \mathbb{N}^*$, it follows that $a_n + a_{n+1} + a_{n+2} = C$, with $C$ being a constant. If $a_5=2$, $a_7=-3$, and $a_9=4$, find the sum $a_1 + a_2 + \ldots + a_{100}$.

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