
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 that $\overrightarrow{i}$, $\overrightarrow{j}$, $\overrightarrow{k}$ are three non-coplanar vectors, the vector $\overrightarrow{a}$ is $\frac{1}{2}\overrightarrow{i} - \overrightarrow{j} + \overrightarrow{k}$ and the vector $\overrightarrow{b}$ is $5\overrightarrow{i} - 2\overrightarrow{j} - \overrightarrow{k}$. Find the vector $4\overrightarrow{a} - 3\overrightarrow{b}$.

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