
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
Compute the number of subsets  $S$  of  $\{0,1,\dots,14\}$  with the property that for each  $n=0,1,\dots,
6$ , either  $n$  is in  $S$  or both of  $2n+1$  and  $2n+2$  are in  $S$ .

*Proposed by Evan Chen*

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