
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
With the vertex of angle θ as the coordinate origin, and the initial side as the non-negative half-axis of the x-axis, establish the Cartesian coordinate system xOy. If the terminal side of angle θ passes through point P(1, -2), then find the value of sin 2θ.

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