
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
Two walls and the ceiling of a room meet at right angles at point \(P\). A fly is in the air three meters from one wall, four meters from the other wall, and seven meters from point \(P\). How many meters is the fly from the ceiling?
A) $2$
B) $3$
C) $\sqrt{24}$
D) $2\sqrt{6}$

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