
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 rectangular plot of land, a man walks in a very peculiar fashion. Labeling the corners  $ABCD$ , he starts at  $A$  and walks to  $C$ . Then, he walks to the midpoint of side  $AD$ , say  $A_1$ . Then, he walks to the midpoint of side  $CD$  say  $C_1$ , and then the midpoint of  $A_1D$  which is  $A_2$ . He continues in this fashion, indefinitely. The total length of his path if  $AB=5$  and  $BC=12$  is of the form  $a + b\sqrt{c}$ . Find  $\displaystyle\frac{abc}{4}$ .

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