
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
In the sequence $\{a_n\}$, if for all $n \in \mathbb{N}^*$, it holds that $a_n = -3a_{n+1}$, and $$\lim_{n \to \infty}(a_{2}+a_{4}+a_{6}+\ldots+a_{2n}) = \frac{9}{2},$$ then the value of $a_1$ is \_\_\_\_\_\_.

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