
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
Rectangle  $ABCD$  has sides  $AB = 3$ ,  $BC = 2$ . Point  $ P$  lies on side  $AB$  is such that the bisector of the angle  $CDP$  passes through the midpoint  $M$  of  $BC$ . Find  $BP$ .

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