
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
From the pole $O$, a ray is drawn that intersects the line $\rho\cos\theta=3$ at point $M$. A point $P$ is taken on $OM$ such that $OM\cdot OP=12$. If $Q$ is a point on the curve $$\begin{cases} x=-1+ \frac { \sqrt {2}}{2}t \\ y=2+ \frac { \sqrt {2}}{2}t\end{cases}$$ (where $t$ is a parameter), find the minimum value of $PQ$.

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