
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 $x$ be a real number such that
\[ x^2 + 9 \left( \frac{x}{x - 3} \right)^2 = 54. \] Find all possible values of $y = \frac{(x - 3)^2 (x + 4)}{3x - 4}.$ Enter all possible values, separated by commas.

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