
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 \( I \) is the incenter of \( \triangle ABC \) and \( 5 \overrightarrow{IA} = 4(\overrightarrow{BI} + \overrightarrow{CI}) \). Let \( R \) and \( r \) be the radii of the circumcircle and the incircle of \( \triangle ABC \) respectively. If \( r = 15 \), then find \( R \).

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