
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
Non-degenerate quadrilateral  $ABCD$  with  $AB = AD$  and  $BC = CD$  has integer side lengths, and  $\angle ABC = \angle BCD = \angle CDA$ . If  $AB = 3$  and  $B \ne D$ , how many possible lengths are there for  $BC$ ?


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