
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
What is the least positive integer  $m$  such that the following is true?

*Given  $\it m$  integers between  $\it1$  and  $\it{2023},$  inclusive, there must exist two of them  $\it a, b$  such that  $1 < \frac ab \le 2.$* \[\mathrm a. ~ 10\qquad \mathrm b.~11\qquad \mathrm c. ~12 \qquad \mathrm d. ~13 \qquad \mathrm e. ~1415\]

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