
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
In the plane rectangular coordinate system $xOy$, the distance between two points $A(x_{1}, y_{1})$ and $B(x_{2}, y_{2})$ is defined as follows: $d(A,B)=|x_{1}-x_{2}|+2|y_{1}-y_{2}|$. If $A(2,1)$, $B(-1,m)$, and $d(A,B)\leqslant 5$, then the range of real number $m$ is ______.

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