
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
The angle bisectors $\mathrm{AD}$ and $\mathrm{BE}$ of the triangle $\mathrm{ABC}$ intersect at point I. It turns out that the area of triangle $\mathrm{ABI}$ is equal to the area of quadrilateral $\mathrm{CDIE}$. Find the maximum possible value of angle $\mathrm{ACB}$.

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