
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
Triangle $ABC$ has $\angle BAC = 45^\circ$, $\angle ACB \geq 90^\circ$, $BC=1$, and $AC \geq AB$. Let $H$, $I$, and $O$ be the orthocenter, incenter, and circumcenter of $\triangle ABC$, respectively. Define $D$ as the midpoint of $BC$. Assume that the area of triangle $BOH$ is the maximum possible. What is $\angle ACB$?
A) $82.5^\circ$
B) $85^\circ$
C) $87.5^\circ$
D) $90^\circ$
E) $95^\circ$

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