
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 \\(\alpha\\) coincides with the origin of the Cartesian coordinate system, its initial side is on the non-negative half-axis of \\(x\\), and its terminal side passes through point \\(P(-1,2)\\), find the value of \\(\sin (2\alpha+ \dfrac {2}{3}\pi)\\).

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