
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
Given a fixed circle $\odot P$ with a radius of 1, the distance from the center $P$ to a fixed line $l$ is 2. Point $Q$ is a moving point on $l$, and circle $\odot Q$ is externally tangent to circle $\odot P$. Circle $\odot Q$ intersects $l$ at points $M$ and $N$. For any diameter $MN$, there is always a fixed point $A$ on the plane such that the angle $\angle MAN$ is a constant value. Find the degree measure of $\angle MAN$.

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