
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
Let the set \( A = \{1, 2, m\} \), where \( m \) is a real number. Define \( B = \{a^2 \mid a \in A\} \) and \( C = A \cup B \). If the sum of all elements in \( C \) is 6, what is the product of all elements in \( C \)?

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