
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
For which values of \(a\) is the point with coordinates \((\sin a, \sin 3a)\) symmetric to the point with coordinates \((\cos a, \cos 3a)\) with respect to the line given by the equation \(x + y = 0\)?

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