
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
Find the smallest positive integer \( m \) such that for any 14-partition \( A = \{1, 2, \cdots, m\} \) into subsets \( A_1, A_2, \cdots, A_{14} \), there always exists a subset \( A_i \) (with \( 1 < i < 14 \)) containing two elements \( a \) and \( b \) where \( b < a \leq \frac{4}{3}b \).

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