
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 sets $B$ and $C$, such that $B$⋃$C=\{1,2,3,4,5,6,7,8,9,10\}$, $B$⋂$C=\varnothing$, and the product of elements in $C$ is equal to the sum of elements in $B$, write down all sets $C$ that satisfy the conditions.

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