
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
Circle $C_1$ has the equation $(x^2+y^2=\frac{4}{25})$, and circle $C_2$ has the equation $((x−\cos ⁡θ)^2+(y−\sin ⁡θ)^2= \frac{1}{25})$ $(θ∈R)$. Let $P$ be any point on circle $C_2$. The two tangents $PM$ and $PN$ are drawn from $P$ to circle $C_1$, with tangent points $M$ and $N$, respectively. Calculate the maximum value of $\angle MPN$.

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