
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 $f(x)$ defined on $\mathbb{R}$ such that for all $x$, $y \in \mathbb{R}$, $f(2xy+3) = f(x) \cdot f(y) - 3f(y) - 6x + 9$, and $f(0) = 3$, the solution set of the inequality $f(x) > x$ is ______.

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