
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 $f(x)= \sqrt {3}\sin x\cos x-\sin ^{2}x$, the graph of $f(x)$ is translated right by $\dfrac {\pi}{12}$ units and then translated up by $2$ units to obtain the graph of $y=g(x)$. If for any real number $x$, $g(\alpha-x)=g(\alpha+x)$ holds, find the value of $g(\alpha+ \dfrac {\pi}{4})+g( \dfrac {\pi}{4})$.

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