
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 curve $f(x)=-{{{e}}^{x}}-x$ (where $e$ is the base of the natural logarithm), let ${{l}\_{1}}$ be the tangent line at any point on the curve. There always exists a point on the curve $g(x)=3ax+2\cos x$ such that its tangent line ${{l}\_{2}}$ is perpendicular to ${{l}\_{1}}$. Find the range of values for the real number $a$.

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