
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 that point $P$ is a common point of circle $O\_1$ and circle $O\_2$, where circle $O\_1$ is defined as $(x-a)^{2}+(y-b)^{2}=b^{2}+1$, and circle $O\_2$ is defined as $(x-c)^{2}+(y-d)^{2}=d^{2}+1$. If $ac=8$, $\frac {a}{b} = \frac {c}{d}$, then the minimum value of the distance between point $P$ and any point $M$ on line $l$: $3x-4y-25=0$ is _____.

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