
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
Let the set M = {A, A_1, A_2, A_3, A_4, A_5}, and define the operation "$\otimes$" on M as: $A_i \otimes A_j = A_k$, where k is the remainder of i+j divided by 4, with i, j = 0, 1, 2, 3, 4, 5. Determine the number of elements a (a ∈ M) that satisfy the equation $(a \otimes a) \otimes A_2 = A$.

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