
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 circle $(x+1)^{2}+y^{2}=4$ with center $C$, and point $P$ is on the line $mx-y-5m+4=0$. If there exists a point $Q$ on the circle such that $\angle CPQ=30^{\circ}$, determine the range of the real number $m$.

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