
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
Find the sum of the integers that belong to the set of values of the function \(f(x) = \log_{2}(5 \cos 2x + 11)\) for \(x \in \left[1.25 \left(\arctan\left(\frac{1}{3}\right)\right) \cos\left(\pi + \arcsin(-0.6)\right), \arctan 2\right]\).

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