
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 sets \( A = \{ x \mid x^2 - 3x + 2 = 0 \} \) and \( C = \{ x \mid x^2 - mx + 2 = 0 \} \), with \( A \cap C = C \), determine the value of the real number \( m \).

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