
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 $ABCDEF$ be a regular hexagon, and let $J, K, L$ be the midpoints of sides $AB$, $CD$, and $EF$ respectively. Suppose there are additional points $M, N, O$ on sides $BC$, $DE$, and $FA$ such that each segment is divided into four equal parts. If the area of $\triangle JKL$ is $100$, what is the area of hexagon $ABCDEF$?

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