
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
Let $P$ be a point inside triangle $ABC$ such that
\[\overrightarrow{PA} + 3 \overrightarrow{PB} + 2 \overrightarrow{PC} = \mathbf{0}.\]
Find the ratio of the area of triangle $ABC$ to the area of triangle $APB$.

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