
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
Given the modified Lucas sequence defined as 2, 5, 7, 12, 19, $\ldots$, where the first term is 2, the second term is 5, and each subsequent term is the sum of the previous two terms, what is the remainder when the $50^{\mathrm{th}}$ term of the sequence is divided by 5?

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