
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 $R$ that satisfies $f(x-3)=-f(x)$. For all ${x_1}, {x_2} \in [0,3]$ and ${x_1} \neq {x_2}$, we have $\frac{f({x_1})-f({x_2})}{{x_1}-{x_2}} > 0$. Determine the correct ordering of $f(49), f(64),$ and $f(81)$.

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