
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 $f(x)=e^{x}-e^{-x}+ln(x+ \sqrt {x^{2}+1})$ (where $e \approx 2.71828$), if $f(x^2+2) + f(-2ax) \geq 0$ holds true for any $x \in [2, +\infty)$, then the range of values for the real number $a$ is $\_\_\_\_\_\_.$

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