
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 triangle \( \triangle ABC \), \( |AB| = 13 \), \( |BC| = 14 \), \( |CA| = 15 \), an internal point \( P \) satisfies
\[ 
\overrightarrow{BP} \cdot \overrightarrow{CA} = 18 \text{ and } \overrightarrow{CP} \cdot \overrightarrow{BA} = 32.
\]
What is \( \overrightarrow{AP} \cdot \overrightarrow{BC} \)?

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