
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
1. Simplify the result of $\overrightarrow{BC} + \overrightarrow{AB} - \overrightarrow{AC}$.
2. Calculate $\dfrac{\tan {15}^{0}}{1-{\tan }^{2}{15}^{0}}$.
3. If $f(\cos x)=\cos 2x$, find the value of $f(\sin \dfrac{π}{12})$.
4. Determine the domain of the function $y=\lg \sin \dfrac{x}{2}$.
5. For the function $f(x)=\left|2\sin (2x- \dfrac{π}{6})+ \dfrac{1}{2} \right|$, find the smallest positive value of $c$ such that $f(x+c)=f(x-c)$ always holds true.

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