
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 \( f(x) = \log_{3}(40 \cos 2x + 41) \) for \( x \in \left[ \frac{5}{3} \arctan \left( \frac{1}{5} \right) \cos (\pi - \arcsin(-0.8)), \arctan 3 \right] \).

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