
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 that the derivative of the function $f(x)$ on its domain $\mathbb{R}$ is $f''(x)$, if the equation $f''(x)=0$ has no solution, and $f[f(x)-2017^{x}]=2017$, when $g(x)=x- \frac{1}{3}\sin 2x+a\sin x$ has the same monotonicity as $f(x)$ on $\mathbb{R}$ in the interval $\left[ \frac{\pi}{3},\pi\right]$, determine the range of the real number $a$.

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