
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
There is a rectangle  $ABCD$  such that  $AB=12$  and  $BC=7$ .  $E$  and  $F$  lie on sides  $AB$  and  $CD$  respectively such that  $\frac{AE}{EB} = 1$  and  $\frac{CF}{FD} = \frac{1}{2}$ . Call  $X$  the intersection of  $AF$  and  $DE$ . What is the area of pentagon  $BCFXE$ ?


Proposed by Minseok Eli Park (wolfpack)

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