
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
Given that \( f(x)=a_{1} x + a_{2} x^{2} + a_{3} x^{3} + \cdots + a_{n} x^{n} \), where \( a_{1}, a_{2}, a_{3}, \cdots, a_{n} \) form an arithmetic sequence, and \( n \) is a positive even number. Also, given \( f(1) = n^{2} \) and \( f(-1) = n \), compare the value of \( f\left(\frac{1}{2}\right) \) to 3.

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