
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 the function $f(x)=\log_{2}(4^{x}+1)-mx$ is an even function.<br/>$(1)$ If $f(x)=1$, find the value of $x$;<br/>$(2)$ If the real number $t$ satisfies $f(t-2) \lt f(2t+2)$, find the range of values for $t$.

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