
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
A combination lock has a 3 number combination, with each number an integer between 0 and 39 inclusive. Call the numbers \( n_{1}, n_{2} \), and \( n_{3} \). If you know that \( n_{1} \) and \( n_{3} \) leave the same remainder when divided by 4, and \( n_{2} \) and \( n_{1}+2 \) leave the same remainder when divided by 4, how many possible combinations are there?

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