
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
Let $f(x) = \log_{4}(4^{x}+1) + ax$, where $a \in \mathbb{R}$.

(1) If function $f(x)$ is an even function defined on $\mathbb{R}$, find the value of $a$.

(2) If the inequality $f(x) + f(-x) \geqslant mt + m$ holds for any $x \in \mathbb{R}$, $t \in [-2, 1]$, find the range of values for the real number $m$.

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