
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 the line $l: 2x - y + 1 = 0$ and points $A(-1, 2)$, $B(0, 3)$, find a point $P$ on $l$ such that the value of $|PA| + |PB|$ is minimum, and find this minimum value.

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