
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 a modified Lucas sequence where the first term is 2, the second term is 5, and each subsequent term is the sum of the two preceding terms. What is the remainder when the $75^{\text{th}}$ term of this modified sequence is divided by 7?

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