
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) $\sin 42^\circ \cos 18^\circ -\cos 138^\circ \cos 72^\circ =$\_\_\_\_\_\_\_\_\_\_

(2) Let the function $f(x)=\begin{cases} x, & x < 1 \\ x^{3}-\frac{1}{x}+1, & x\geqslant 1 \end{cases}$, then $f(\frac{1}{f(2)})=$\_\_\_\_\_\_\_\_\_\_

(3) The smallest positive period of the function $f(x)=\sin \left(3x+ \frac{\pi}{4}\right) $ is          .

(4) In isosceles $\Delta ABC$ with apex angle $A=\frac{2\pi }{3}$ and $|BC|=2\sqrt{3}$, then $\overrightarrow{BA}\cdot \overrightarrow{AC}=$\_\_\_\_\_\_\_\_\_\_

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