
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
Points \( A, B, C, D \) are chosen in the plane such that segments \( AB, BC, CD, DA \) have lengths \( 2, 7, 5, 12 \) , respectively. Let \( m \) be the minimum possible value of the length of segment \( AC \) and let \( M \) be the maximum possible value of the length of segment \( AC \). What is the ordered pair \((m, M)\)?

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