
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
Let \\(P(x,y)\\) be a point on the curve \\(C\\): \\( \sqrt { \frac {x^{2}}{25}}+ \sqrt { \frac {y^{2}}{9}}=1\\), with \\(F_{1}(-4,0)\\) and \\(F_{2}(4,0)\\). Find the maximum value of \\(|PF_{1}|+|PF_{2}|\\).

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