
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
We call a set of positive integers "tyû-de-jó" if there are no two numbers in the set whose difference is 2. How many "tyû-de-jó" subsets are there of the set $\{1,2,3, \ldots, 10\}$?

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