
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
Let \\(\omega\\) be a positive real number. The function \\(f(x)=2\cos \omega x\\) is decreasing on the interval \\(x \in \left[0, \frac{2\pi}{3}\right]\\) and has a minimum value of \\(1\\). Determine the value of \\(\omega\\).

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