
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 \(A B C D E F\) be a regular hexagon of area 1. Let \(M\) be the midpoint of \(D E\). Let \(X\) be the intersection of \(A C\) and \(B M\), let \(Y\) be the intersection of \(B F\) and \(A M\), and let \(Z\) be the intersection of \(A C\) and \(B F\). If \([P]\) denotes the area of polygon \(P\) for any polygon \(P\) in the plane, evaluate \([B X C]+[A Y F]+[A B Z]-[M X Z Y]\).

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