
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 \( a, b, c \) be non-negative real numbers satisfying
\[ a + b + c = 8 \]
and
\[ ab + bc + ca = 16.\]
Let \( m = \min \{ ab, bc, ca \} \). Find the maximum possible value of \( m \).

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