
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 $f(x)=\sin x\cos x+ \sqrt {3}\cos ^{2}x- \dfrac { \sqrt {3}}{2}$, the graph of $f(x)$ is translated right by $\dfrac {\pi}{6}$ units and then translated up by $1$ unit to obtain the graph of $y=g(x)$. If for any real number $x$, $g(a-x)=g(a+x)$ holds, find the value of $g\left(a+\dfrac {\pi}{4}\right)$.

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