
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
A chord $OA$ is drawn through the origin $O$ on the circle $x^{2}+y^{2}-8x=0$.

(1) Find the trajectory equation of the midpoint $M$ of the chord $OA$.

(2) Extend $OA$ to $N$ such that $|OA|=|AN|$, find the trajectory equation of point $N$.

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