
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
In a Cartesian coordinate system, given points \( A(-2,-3) \), \( B(4,-1) \), \( C(m, 0) \), and \( D(n, n) \), find the minimum value of \( \mathrm{AB}+\mathrm{BC}+\mathrm{CD}+\mathrm{AD} \).

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