
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
Let vector $\overrightarrow{a}=(\cos x,-\sin x)$, $\overrightarrow{b}=(-\cos \left( \frac {\pi}{2}-x\right),\cos x)$, and $\overrightarrow{a}=t \overrightarrow{b}$, $t\neq 0$, calculate the value of $\sin 2x$.

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