
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 \( \mathrm{f} \) be a function defined on non-zero real numbers such that
$$
\frac{27 \mathrm{f}(-x)}{x} - x^{2} \mathrm{f}\left(\frac{1}{x}\right) = -2 x^{2},
$$
for all \( x \neq 0 \). Find \( \mathrm{f}(3) \).

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