
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) Given the function $f(x)=\begin{cases} & \log_{\frac{1}{2}}x,x > 0, \\ & \cos x,x\leqslant 0, \\ \end{cases}$ find the value of $f(f(-\frac{\pi }{3}))=\_\_\_\_\_\_\_\_\_\_.$

(2) Given real numbers $x$ and $y$ that satisfy the system of inequalities $\begin{cases} & x-2y+1\geqslant 0, \\ & x < 2, \\ & x+y-1\geqslant 0, \\ \end{cases}$ find the range of values for $z=3x-4y$.

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