
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 two non-collinear vectors $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$, let vector $\overrightarrow{a} = 3\overrightarrow{e_{1}} - 2\overrightarrow{e_{2}}$ and vector $\overrightarrow{b} = \overrightarrow{e_{2}} - 2\overrightarrow{e_{1}}$. Then, the expression $\left(\frac{1}{3}\overrightarrow{a} + \overrightarrow{b}\right) + \left(\overrightarrow{a} - \frac{3}{2}\overrightarrow{b}\right) + \left(2\overrightarrow{b} - \overrightarrow{a}\right) = $ ______.

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