
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 vectors $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ are unit vectors with an angle of $\dfrac{2π}{3}$ between them, and that $\overrightarrow{a} = 3\overrightarrow{e_{1}}$ and $\overrightarrow{b} = \overrightarrow{e_{1}} - \overrightarrow{e_{2}}$, find the projection of vector $\overrightarrow{b}$ onto the direction of vector $\overrightarrow{a}$.

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