
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 $\overrightarrow{i}$, $\overrightarrow{j}$, and $\overrightarrow{k}$ are unit vectors in space that are mutually perpendicular, and $\overrightarrow{a}=\overrightarrow{i}+2\overrightarrow{j}-\overrightarrow{k}$, $\overrightarrow{b}=3\overrightarrow{i}-\overrightarrow{j}+4\overrightarrow{k}$, find $\overrightarrow{a}\cdot \overrightarrow{b}$.

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