
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
Alice is standing on the circumference of a large circular room of radius  $10$ . There is a circular pillar in the center of the room of radius  $5$  that blocks Alice’s view. The total area in the room Alice can see can be expressed in the form  $\frac{m\pi}{n} +p\sqrt{q}$ , where  $m$  and  $n$  are relatively prime positive integers and  $p$  and  $q$  are integers such that  $q$  is square-free. Compute  $m + n + p + q$ . (Note that the pillar is not included in the total area of the room.)
![Image](https://cdn.artofproblemsolving.com/attachments/1/9/a744291a61df286735d63d8eb09e25d4627852.png)

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