
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
Let \( M=\{(x, y) \mid x=\cos \theta, y=\sin \theta, 0<\theta<\pi\} \) and \( N=\{(x, y) \mid y=x+m\} \). If \( M \cap N \neq \varnothing \), what is the range of the real number \( m \)?

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