
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 on line $l\_1$: $x+y+3=0$, and the line $l\_2$ passing through point $P$ intersects with the curve $C$: $(x-5)^{2}+y^{2}=16$ at only one point $M$, find the minimum value of $|PM|$.

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