
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 of area 1. Let \( M \) be the midpoint of \( DE \). Let \( X \) be the intersection of \( AC \) and \( BM \), \( Y \) be the intersection of \( BF \) and \( AM \), and \( Z \) be the intersection of \( AC \) and \( BF \). Evaluate the expression \( [BXC] + [AYF] + [ABZ] - [MXZY] \), where \([P]\) denotes the area of polygon \(P\).

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