
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 number of subsets \( S \) of \(\{1,2, \ldots, 48\}\) satisfying both of the following properties:
- For each integer \(1 \leq k \leq 24\), exactly one of \(2k-1\) and \(2k\) is in \(S\).
- There are exactly nine integers \(1 \leq m \leq 47\) so that both \(m\) and \(m+1\) are in \(S\).

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