
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 a \(3 \times 3\) square \(ABCD\), point \(E\) is located one third of the way along \(\overline{AB}\) from \(A\) to \(B\), and point \(F\) is located one third of the way along \(\overline{BC}\) from \(B\) to \(C\). Line segments \(\overline{AF}\) and \(\overline{DE}\) intersect at point \(I\), and line segments \(\overline{BD}\) and \(\overline{AF}\) intersect at point \(H\). Determine the area of quadrilateral \(BEIH\).

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