
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 tangent line $l$ at point $(1, 2)$ on the curve $y=x^2+1$ is given. Find the shortest distance between any point $P$ on line $l$ and any point $Q$ on the circle $x^2+y^2+4x+3=0$.

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