
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 functions $f(x)= \frac {x+1}{x^{2}}$ and $g(x)=\log _{2}x+m$, if for $\forall x_{1}\in[1,2]$, $\exists x_{2}\in[1,4]$ such that $f(x_{1})\geqslant g(x_{2})$, then the range of $m$ is ______.

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