
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
Given the universal set $U=\{1,2,3,4,5,6,7,8,9,10\}$, find the number of sets $A\subseteq U$ that satisfy the conditions: $A\subseteq U$, if $x\in A$, then $2x\notin A$, and if $x\in \overline{A}$, then $2x\notin \overline{A}$.

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