
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
Isosceles triangle  $\triangle{ABC}$  has  $\angle{ABC}=\angle{ACB}=72^\circ$  and  $BC=1$ . If the angle bisector of  $\angle{ABC}$  meets  $AC$  at  $D$ , what is the positive difference between the perimeters of  $\triangle{ABD}$  and  $\triangle{BCD}$ ?

*2019 CCA Math Bonanza Tiebreaker Round #2*

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