
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 Yule log is shaped like a right cylinder with height  $10$  and diameter  $5$ . Freya cuts it parallel to its bases into  $9$  right cylindrical slices. After Freya cut it, the combined surface area of the slices of the Yule log increased by  $a\pi$ . Compute  $a$ .


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