
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 that the area of triangle $\triangle ABC$ is 1, points $B_{1}$, $B_{2}$, $C_{1}$, and $C_{2}$ are trisection points of sides $AB$ and $AC$ respectively. Connect $B_{1}C$, $B_{2}C$, $BC_{1}$, and $BC_{2}$. Find the area of the quadrilateral they form.

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