
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 parallelogram \( ABCD \), the bisector of angle \( \angle ABC \) intersects side \( AD \) at point \( P \). It is given that \( PD = 5 \), \( BP = 6 \), and \( CP = 6 \). What is the length of side \( AB \)?

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