
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 the lines ${l}_{1}:x-y+5=0$ and ${l}_{2}:x+4=0$, and the parabola $C:{y}^{2}=16x$, let $P$ be a moving point on $C$. The minimum value of the sum of the distances from $P$ to ${l}_{1}$ and ${l}_{2}$ is _______.

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