
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
Given points \( A(9, 1) \), \( B(2, 0) \), \( D(1, 5) \), and \( E(9, 7) \) on the coordinate plane, find the area of the pentagon \( ABCDE \), where \( C \) is the intersection point of lines \( AD \) and \( BE \).

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