
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 \( f(x) \) and \( g(x) \) are two quadratic functions both with a leading coefficient of 1, where \( g(6) = 35 \) and \( \frac{f(-1)}{g(-1)} = \frac{f(1)}{g(1)} = \frac{21}{20} \), what is \( f(6) \)?

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