
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 that $\sin 2θ=2\cos θ$, find the value of:

(I) $\dfrac{6\sin θ+\cos θ}{3\sin θ-2\cos θ}$;

(II) $\dfrac{{\sin }^{2}θ+2\sin θ\cos θ}{2{\sin }^{2}θ-{\cos }^{2}θ}$.

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