
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 system of equations involving \( x \) and \( y \):
$$
\left\{\begin{array}{l}
\sin x = m \sin^3 y, \\
\cos x = m \cos^3 y
\end{array}\right.
$$
If real solutions exist, what is the range of values for the positive real number \( m \)?

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