
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 $f$ defined on $\mathbb{R}$ that is an even function and satisfies $f(x+1)=f(x-1)$, and is monotonically increasing in the interval $[0,1]$, determine the relationship among $f\left(-\frac{3}{2}\right)$, $f(1)$, and $f\left(\frac{4}{3}\right)$.

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