
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
Translate the curve $y \cos x + 2y - 1 = 0$ by moving it right along the $x$-axis by $\frac{\pi}{2}$ units and then down along the $y$-axis by 1 unit. The equation of the resulting curve is ($\quad$).

A) $(1 - y) \sin x + 2y - 3 = 0$
B) $(y - 1) \sin x + 2y - 3 = 0$
C) $(y + 1) \sin x + 2y + 1 = 0$
D) $-(y + 1) \sin x + 2y + 1 = 0$

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