
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
Solve the equation \( 2 \sqrt{2} \sin^{3}\left(\frac{\pi x}{4}\right) = \cos\left(\frac{\pi}{4}(1 - x)\right) \). 

How many solutions of this equation satisfy the condition \( 0 \leq x \leq 2020 \)?

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