
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 points $A_1(a_1,1)$, $A_2(a_2,2)$, ..., $A_n(a_n,n)$ $(n\in\mathbb{N}^*)$ are on the graph of the function $y=\log_{\frac{1}{3}}x$, the general term formula for the sequence $\{a_n\}$ is ______; Let $O$ be the origin, and point $M_n(a_n,0)$ $(n\in\mathbb{N}^*)$, then among the triangles $\triangle OA_1M_1$, $\triangle OA_2M_2$, ..., $\triangle OA_nM_n$, the maximum area is ______.

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