
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 $\omega > 0$, the graph of the function $y = 2\cos(\omega x + \frac{\pi}{5}) - 1$ overlaps with the original graph after shifting right by $\frac{5\pi}{4}$ units. What is the minimum value of $\omega$?

A) $\frac{8}{5}$
B) $\frac{6}{5}$
C) $\frac{4}{5}$
D) $\frac{2}{5}$

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