
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 real-coefficient equation $x^2 - 2ax + a^2 - 4a + 4 = 0$ has two complex roots $x_1$ and $x_2$, and $|x_1| + |x_2| = 3$, find the value of the real number $a$.

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