
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 a quadratic equation $x^{2}+bx+c=0$. Choose one set of values for $b$ and $c$ from the following four options, such that the equation has two distinct real roots, and solve the equation.<br/>①$b=2$,$c=1$;<br/>②$b=3$,$c=1$;<br/>③$b=3$,$c=-1$;<br/>④$b=2$,$c=2$.<br/>Note: If multiple sets of conditions are chosen for separate answers, the first answer will be scored.

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