
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
The function $y=f(x)$ is an even function defined on $\mathbb{R}$, and for any real number $x$, $f(x+1)=f(x-1)$ holds. It is known that when $x \in [1, 2]$, $f(x)=\log_{a}x$.  
(I) Find the expression of $f(x)$ when $x \in [-1, 1]$.  
(II) If $f(0)=1$, solve the inequality $f(x) > \frac{1}{2}$ on the interval $[-1, 1]$.

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