
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
When \(0 < a < 1\), the solution to the system of inequalities \(\left\{\begin{array}{l}\log_{a}\left|x-\frac{\pi}{3}\right|>\log_{a}\frac{2\pi}{3}, \\ \cos x \geqslant 0\end{array}\right.\) is:

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