
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
There is a sequence of natural numbers where, starting from the third number, each number is the sum of the previous two numbers. It is known that the third number is 7, and the 2014th number leaves a remainder of 1 when divided by 4. Determine all possible values of the first number.

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