
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
Find the value(s) of the real number $a$ such that the line passing through the point $P(1,2)$ is tangent to the circle $x^{2}+y^{2}=1$ and is perpendicular to the line $ax+y-1=0$.

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