
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 an acute $\triangle ABC$ with circumcenter $O$. Line $AO$ intersects $BC$ at point $D$. Let $E$ and $F$ be the circumcenters of $\triangle ABD$ and $\triangle ACD$, respectively. If $AB > AC$ and $EF = BC$, then $\angle C - \angle B = \qquad$

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