
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 a triangle $ABC$ with angles $A$, $B$, $C$ and their corresponding sides $a$, $b$, $c$, and the area of the triangle is $S_{\triangle ABC}=\frac{\sqrt{3}}{12}a^2$. Determine the range of real numbers $m$ that satisfy the equation $\sin^2 B + \sin^2 C = m \sin B \sin C$.

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