
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
Let the function \( f(x) \) satisfy the relation \( a f\left(x^{n}\right) + f\left(-x^{n}\right) = b x \), where \( a^{2} \neq 1 \) and \( n \) is an odd number. Find \( f(x) \).

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