
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
In the coordinate plane, the points $A(0, 2)$, $B(1, 7)$, $C(10, 7)$, and $D(7, 1)$ are given. Find the area of the pentagon $ABCDE$, where $E$ is the intersection point of the lines $AC$ and $BD$.

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