
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 a function \( f(x) \) that satisfies for any real numbers \( x \) and \( y \):
\[ f(x+y) = f(x) + f(y) + 6xy \]
and \( f(-1)f(1) \geq 9 \),
find \( f\left(\frac{2}{3}\right) \).

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