
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
Let  $2000 < N < 2100$  be an integer. Suppose the last day of year  $N$  is a Tuesday while the first day of year  $N+2$  is a Friday. The fourth Sunday of year  $N+3$  is the  $m$ th day of January. What is  $m$ ?

*Based on a proposal by Neelabh Deka*

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