
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 that point $P$ lies on the parabola $y^{2}=6x$, and the distance from point $P$ to line $l$: $3x-4y+26=0$ is $d_{1}$.
(1) Find the minimum value of $d_{1}$ and the coordinates of point $P$ at this time;
(2) If the distance from point $P$ to the parabola is $d_{2}$, find the minimum value of $d_{1}+d_{2}$.

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