
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
Consider the Lucas sequence, where the first term is 1, the second term is 3, and each term thereafter is the sum of the previous two terms. Determine the remainder when the $52^{\mathrm{th}}$ term of the sequence is divided by 5.

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