
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 $f(x)$ is a function defined on $(0,+∞)$, and for any positive numbers $x$ and $y$, $f(x+y)=f(x)f(y)$, and when $x > 1$, $f(x) > 2$, $f(2)=4$. Solve for $f(x^{2}) > 2f(x+1)$.

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