
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 the domain of the function $f(x)$ is $\mathbb{R}$, and for all $x \in \mathbb{R}$, $f(-x) = f(x)$ holds.
1. If $x \geq 0$, $f(x) = (\frac{1}{2})^x$, find the solution set of the inequality $f(x) > \frac{1}{4}$.
2. If $f(x+1)$ is an even function, and when $x \in [0, 1]$, $f(x) = 2^x$, find the analytical expression of $f(x)$ on the interval $[2015, 2016]$.

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