
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
The graph of the function $y = \sin 2x$ is translated $\frac{\pi}{4}$ units to the right and then 1 unit up. Determine the formula corresponding to the transformed graph.
A) $y = 2\sin^{2}x$
B) $y = 2\cos^{2}x$
C) $y = \sin(2x - \frac{\pi}{4}) + 1$
D) $y = -\cos 2x$

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