
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) Find the value of $\sin(-1740^{\circ})$.
(2) A high school wants to understand the physical growth status of 800 freshmen. They use systematic sampling to select 50 students for examination. The students are numbered from 1 to 800. It is known that the 17th group's drawn number is 263. What is the number drawn by the first group using simple random sampling?
(3) Given angle $A$ is an internal angle of $\triangle ABC$, and $\sin A + \cos A = \frac{3}{5}$, find the value of $\sin A - \cos A$.
(4) Find the monotonically increasing interval of the function $y = \log_2 \sin(x + \frac{\pi}{3})$.

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