
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 set $U=\{0, 1, 2, 3\}$, and $A=\{x \in U | x^2 + mx = 0\}$,

(1) If $\complement_U A = \{1, 2\}$, find the value of the real number $m$;

(2) If the set $A$ is a singleton (i.e., the set contains only one element), find the value of the real number $m$.

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