
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 $\theta$ is at the origin of coordinates, and its initial side is the positive half-axis of the $x$-axis, if $P(4, y)$ is a point on the terminal side of angle $\theta$, and $\sin \theta = -\dfrac{2\sqrt{5}}{5}$, find the value of $y$.

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