
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 the orthogonal projection of the origin in the right-angle coordinate system be on the line

$$
\frac{x}{a}+\frac{y}{b}=1
$$

at point $P$. What is the locus of the points $P$ if the line moves in such a way that $\frac{1}{a^{2}}+\frac{1}{b^{2}}$ remains constant?

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