
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
If the tangent line at point $P$ of the function $y_{1}=2\sin x$ ($x\in[0,2\pi)$) is parallel to the tangent line at point $Q$ of the function $y_{2}=2 \sqrt {x}\left( \dfrac {x}{3}+1\right)$, find the slope of line $PQ$.

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