
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)** Solve the equation  $ x^2-x+2\equiv 0\pmod 7. $ **b)** Determine the natural numbers  $ n\ge 2 $  for which the equation  $ x^2-x+2\equiv 0\pmod n $  has an unique solution modulo  $ n. $ 

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