
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
The quadrangular pyramid \(P-ABCD\) has a base \(ABCD\) in the shape of a rhombus with a vertex angle of \(60^\circ\). Each lateral face forms an angle of \(60^\circ\) with the base. There is a point \(M\) inside the pyramid such that the distances from \(M\) to the base and each of the lateral faces are all equal to 1. What is the volume of the pyramid?

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