
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
In the rectangular coordinate system $(xOy)$, the point $P(t^{2},2t)$ is parameterized by $t$. If the origin $O$ is taken as the pole and the positive semi-axis of the $x$-axis as the polar axis to establish a polar coordinate system, the polar equation of the line $l$ is $ρ\cos θ-ρ\sin θ+2=0$.

(1) Find the trajectory equation of point $P$.

(2) Find a point $P$ such that its distance to line $l$ is the smallest, and find the minimum value.

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