
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 equation of circle $C_1$ is $$(x-3)^{2}+y^{2}= \frac {4}{25}$$, and the equation of circle $C_2$ is $$(x-3-\cos\theta)^{2}+(y-\sin\theta)^{2}= \frac {1}{25} (\theta\in\mathbb{R})$$. A line through any point $P$ on $C_2$ forms two tangents $PM$ and $PN$ to circle $C_1$, with the points of tangency being $M$ and $N$, respectively. The maximum value of $\tan(\angle MPN)$ is \_\_\_\_\_\_.

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