
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 a function $y=f(x)$, every point on its graph has the ordinate (y-coordinate) expanded to four times the original value and the abscissa (x-coordinate) expanded to twice the original value. Then, the resulting graph is translated leftward by $\dfrac{\pi}{2}$ along the x-axis. If this new curve is identical to the graph of $y=2\sin x$, determine the expression for the known function $y=f(x)$.

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