
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 $f(x)=2\sin (2x+ \frac {\pi}{3})$ and $g(x)=m\cos (2x- \frac {\pi}{6})-2m+3$, with $m > 0$, find the range of the real number $m$ such that for any $x_{1}\in[0, \frac {\pi}{4}]$, there exists $x_{2}\in[0, \frac {\pi}{4}]$ such that $g(x_{1})=f(x_{2})$ holds.

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