
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 a parabola $y^2=2px$ with focus $F$, let $A(x_1, y_1)$ and $B(x_2, y_2)$ be two moving points on the parabola. If $x_1+x_2+p=\frac{2\sqrt{3}}{3}|AB|$, find the maximum value of $\angle AFB$.

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