
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 the parabola \( y^{2} = 2px \) (where \( p > 0 \)), let \( A \) and \( B \) be two points on the parabola other than the vertex \( O \). Denote \( \angle AOB = \theta \) \(\left(\theta \neq 90^{\circ}\right)\). If the area of triangle \( AOB \) is \( m \tan \theta \), find the maximum value of \( \tan \theta \) when \( m \) is minimized.

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