
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

If \( x \leq 90^{\circ} \) and \( \sin y = \frac{3}{4} \sin x \), then it must be shown that

$$
y > \frac{x}{2}
$$

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