
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
Does there exist a quadratic function \( f(x) \) such that the following conditions are satisfied?
1. When \( |x| \leqslant 1 \), \( |f(x)| \leqslant 1 \).
2. \( |f(2)| \geqslant 7 \).

If such a function exists, find all such \( f(x) \). If none exist, provide an explanation.

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