
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 $P$ is any point on the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a > b > 0)$, $F\_{1}$, $F\_{2}$ are its two foci, $O$ is the coordinate origin, and $\overrightarrow{{OQ}}=\overrightarrow{PF\_{1}}+\overrightarrow{PF\_{2}}$, find the trajectory equation of the moving point $Q$.

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