
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 that there always exists a line $l$ passing through point $P(m, 2)$ that intersects circle $C: x^2+y^2=1$ at points $A$ and $B$ such that for any point $Q$ in the plane, it satisfies $\overrightarrow{QP} + \overrightarrow{QB} = 2\overrightarrow{QA}$, determine the range of the real number $m$.

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