
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 that \( P \) is a point on a sphere \( O \) with radius \( r \), three mutually perpendicular chords \( PA \), \( PB \), and \( PC \) are drawn through \( P \). If the maximum distance from point \( P \) to the plane \( ABC \) is 1, then \( r \) equals \(\quad\)

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