
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 $f(x)=\log _{a}(a^{2x}+1)+kx$ where $(a > 0, a \neq 1)$ is an even function.<br/>$(1)$ Find the value of $k$;<br/>$(2)$ Let $g(x)=2a^{f(x)+x}-5a^{x}$. If $g(x) \leqslant 0$ holds for all $x \in [-1,2]$, find the range of values for $a$.

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