
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 that the union of sets \( A, B, C \) (not necessarily distinct) is \( A \cup B \cup C = \{1,2,3,4,5,6,7,8,9,10\}\), find the number of ordered triples \((A, B, C)\) under this condition. Express your answer in the form \( a^{b} \).

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