
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) The domain of the function $y=\tan (2x- \frac{\pi}{3})$ is              .

(2) In quadrilateral $ABCD$, $| \overrightarrow{AB} |=8$, $| \overrightarrow{AD} |=15$, and $| \overrightarrow{AB} - \overrightarrow{AD} |=| \overrightarrow{AB} + \overrightarrow{AD} |$. Then $| \overrightarrow{AB} + \overrightarrow{AD} |=$           .

(3) Let $a=\sin 33^{\circ}$, $b=\cos 55^{\circ}$, $c=\tan 35^{\circ}$, then sort $a$, $b$, $c$ from largest to smallest          .

(4) If $\cos (2\theta- \frac{\pi}{6}) < \frac{ \sqrt{3}}{2},\theta\in[0,\pi]$, then the range of $\theta$ is                .

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