
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 points $F_{1}$ and $F_{2}$ are two foci of the ellipse $C:\frac{{x}^{2}}{25}+\frac{{y}^{2}}{9}=1$, and the point $M$ with an x-coordinate of $4$ lies on the ellipse $C$, then the perimeter of $\triangle F_{1}MF_{2}$ is ______.

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