
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
Define an even function $f(x)$ on $\mathbb{R}$ that satisfies $f(x-3)=-f(x)$. For any $x_{1}, x_{2} \in [0,3]$ and $x_{1} \neq x_{2}$, it holds that $\dfrac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}} > 0$. Determine the relationship between $f(49)$, $f(64)$, and $f(81)$.

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