
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 a line $l: ρ\cos θ=4$, draw a line from the pole $O$ that intersects with $l$ at point $M$. Take a point $P$ on $OM$ such that $|OM|·|OP|=12$.

(1) Find the equation of the trajectory of point $P$.
(2) Let $R$ be any point on $l$, find the minimum value of $|RP|$.

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