
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
Three concentric circles have radii $5$ meters, $15$ meters, and $25$ meters respectively. Calculate the total distance a beetle travels, which starts at a point $P$ on the outer circle, moves inward along a radius to the middle circle, traces a one-third arc of the middle circle, then travels radially to the inner circle, follows a half arc of the inner circle, and finally moves directly through the center to the opposite point on the outer circle.

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