
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
A circular cone has vertex \( I \), a base with radius 1, and a slant height of 4. Point \( A \) is on the circumference of the base and point \( R \) is on the line segment \( IA \) with \( IR = 3 \). Shahid draws the shortest possible path starting at \( R \), traveling once around the cone, and ending at \( A \). If \( P \) is the point on this path that is closest to \( I \), what is the length \( IP \)?

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