
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 lines $l\_1$: $4x-3y+16=0$ and $l\_2$: $x=-1$, and a moving point $P$ on the parabola $y^{2}=4x$, let $d\_1$ be the distance from point $P$ to line $l\_1$, and $d\_2$ the distance from point $P$ to line $l\_2$. Find the minimum value of $d\_1 + d\_2$.

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