
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
(Additional Question)  
(1) Let set $A=\{1,2,3,\ldots,10\}$, find the sum of the elements of all non-empty subsets of set $A$.  
(2) In the interval $[2,3]$, the number of real roots of the equation $\log_{2}\log_{3}x=\log_{3}\log_{2}x$ is $\boxed{\text{answer}}$.

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