
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
Point $\mathrm{P}$ moves on the circle $(\mathrm{x}-2)^{2}+(\mathrm{y}-1)^{2}=1$. The vector $\overrightarrow{\mathrm{PO}}$ (where $\mathrm{O}$ is the origin) rotates counterclockwise by $90^{\circ}$ around point $\mathrm{P}$ to obtain $\overrightarrow{\mathrm{PQ}}$. Find the equation of the locus of point $\mathrm{Q}$.

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