
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 the function $y = 2\cos 2x$ and the function $y = 2\cos(2x - \frac{\pi}{4})$, determine the horizontal shift required to obtain the graph of $y = 2\cos(2x - \frac{\pi}{4})$ from the graph of $y=2\cos 2x$.

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