
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

Find the form of all quadratic trinomials \( f(x) = ax^2 + bx + c \), where \( a, b, c \) are given constants and \( a \neq 0 \), such that for all values of \( x \), the condition \( f(3.8x - 1) = f(-3.8x) \) holds.

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