
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 the vertex of angle \( θ \) is at the origin of coordinates, its initial side coincides with the positive half-axis of \( x \), and its terminal side is on the line \( 3x-y=0 \), simplify the expression \( \dfrac{\sin \left( \left. \dfrac{3π}{2}+θ \right. \right)+2\cos (π-θ)}{\sin \left( \left. \dfrac{π}{2}-θ \right. \right)-\sin (π-θ)} \).

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