
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
If $M$ is a moving point on the ellipse $C_{1}: \frac{x^{2}}{25}+ \frac{y^{2}}{9}=1$, and $N$ is a moving point on the ellipse $C_{2}: \frac{x^{2}}{9}+ \frac{y^{2}}{25}=1$, then the maximum value of $\overrightarrow {OM}\cdot \overrightarrow {ON}$ is $\_\_\_\_\_\_$.

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