
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 $$\overrightarrow {a}=( \sqrt {3}\sin x，\cos x+\sin x)， \overrightarrow {b}=(2\cos x，\sin x-\cos x)，f(x)= \overrightarrow {a}\cdot \overrightarrow {b}$$．  
(1) Find the monotonic intervals of the function $f(x)$;  
(2) When $$x\in[ \frac {5\pi}{24}， \frac {5\pi}{12}]$$, for any $t\in\mathbb{R}$, the inequality $mt^2+mt+3\geq f(x)$ always holds, find the range of the real number $m$.

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