
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
The last digits of the squares of natural numbers will be \(0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, \ldots\). Justify the periodicity of this sequence and the symmetry of the period.

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