
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

Construct polynomials \( f(x) \) of degree no higher than 2 that satisfy the conditions:
a) \( f(0)=1, f(1)=3, f(2)=3 \)

b) \( f(-1)=-1, f(0)=2, f(1)=5 \)

c) \( f(-1)=1, f(0)=0, f(2)=4 \).

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