
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 fixed points $A(0,0)$, $B(0,\frac{\sqrt{2}}{2})$, the line $l_{1}$: $kx-y+2k+3=0$, and the line $l_{2}$: $x+ky+3k+2=0$, find the minimum value of $3|PO|+2|PQ|$, where $P$ is the intersection point of $l_{1}$ and $l_{2}$.

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