
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
We have a five-digit positive integer  $N$ . We select every pair of digits of  $N$  (and keep them in order) to obtain the  $\tbinom52 = 10$  numbers  $33$ ,  $37$ ,  $37$ ,  $37$ ,  $38$ ,  $73$ ,  $77$ ,  $78$ ,  $83$ ,  $87$ .  Find  $N$ .

*Proposed by Lewis Chen*

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