
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
In the mathematics club, the teacher thought of a polynomial function of degree at most \( n \). The students can ask for the value of the function at any real number. How many substitution values are needed to determine with certainty whether the function is even?

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