
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 equation \( 3.443 A = \operatorname{ctg} \frac{5 \pi}{4} - 2 \sin^{2}\left( \frac{5 \pi}{2} + \frac{1}{2} \arcsin \frac{2 \sqrt{2} - 1}{3} \right) \), find the value of \( A \).

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