
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
Given triangle $\triangle ABC$, $P$ and $Q$ are points on sides $AB$ and $BC$ respectively, such that $\overrightarrow{AP}=\frac{1}{3}\overrightarrow{AB}$ and $\overrightarrow{BQ}=\frac{1}{3}\overrightarrow{BC}$. If $\overrightarrow{AB}=\overrightarrow{a}$ and $\overrightarrow{AC}=\overrightarrow{b}$, find the vector $\overrightarrow{PQ}$.

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