
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 the graph of $f(x) = \sin(\omega x + \frac{\pi}{3})$ ($\omega > 0$) intersects the graph of $y = -1$ at two adjacent points with distance $\pi$ between them, determine the horizontal shift required to transform the graph of $y=\cos 2x$ into the graph of $y=f(x)$.

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