
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 moving point \( P \) on the parabola \( y^2 = 4x \), with focus \( F(1,0) \) and the origin \( O \) as the coordinate origin, find the maximum value of the inradius \( r \) of triangle \( \triangle OPF \).

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