
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 \(m\) be a positive integer, and let \(T\) denote the set of all subsets of \(\{1, 2, \ldots, m\}\). Call a subset \(S\) of \(T\) \(\delta\)-good if for all \(s_1, s_2 \in S\), \(s_1 \neq s_2\), \(|\Delta(s_1, s_2)| \geq \delta m\), where \(\Delta\) denotes symmetric difference (the symmetric difference of two sets is the set of elements that are in exactly one of the two sets). Find the largest possible integer \(s\) such that there exists an integer \(m\) and a \(\frac{1024}{2047}\)-good set of size \(s\).

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