
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
Let $m \in \mathbb{R}$, the line $x + my = 0$ intersects with the line $mx - y - 2m + 4 = 0$ at point $P(x, y)$. Find the maximum distance from point $P$ to the line $l: (x-1)\cos\theta + (y-2)\sin\theta = 3$.

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