
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
Given the function $f(x)=A\sin(\omega x+\varphi)$, with $A>0$, $\omega>0$, and $|\varphi|<\frac{\pi}{2}$, the coordinates of two adjacent highest and lowest points are ($\frac{\pi}{8}$,1) and ($\frac{5\pi}{8}$,-3) respectively. Determine the range of the function $f(x)$ on the interval $[-\frac{\pi}{2},-\frac{\pi}{24}]$.

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