
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 a point on the line $x+y-2=0$, and a tangent line is drawn from point $p$ to the circle $O$: $x^{2}+y^{2}=1$ with the points of tangency being $M$ and $N$. If $\angle MPN=90^{\circ}$, calculate the number of such points $p$.

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