
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 real numbers \( a, b, c \) such that \( a + b + c = 2 \) and \( abc = 4 \).

1. Find the minimum value of the maximum among \( a, b, \) and \( c \).
2. Find the minimum value of \( |a| + |b| + |c| \).

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