
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 vectors $\overrightarrow{a}=(\cos \dfrac {3x}{2},\sin \dfrac {3x}{2})$ and $\overrightarrow{b}=(\cos \dfrac {x}{2},-\sin \dfrac {x}{2})$, for the function $f(x)= \overrightarrow{a} \cdot \overrightarrow{b} - m| \overrightarrow{a}+ \overrightarrow{b}|+1$, where $x\in\left[- \dfrac {\pi}{3}, \dfrac {\pi}{4}\right]$ and $m\in\mathbb{R}$:
1. Find the value of $f\left( \dfrac {\pi}{6}\right)$ when $m=0$;
2. If the minimum value of $f(x)$ is $-1$, find the value of the real number $m$;
3. Determine if there exists a real number $m$ such that the function $g(x)=f(x)+ \dfrac {24}{49}m^{2}$, for $x\in\left[- \dfrac {\pi}{3}, \dfrac {\pi}{4}\right]$, has four different zeros. If such an $m$ exists, find its range; if not, explain why.

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