
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
Let $e_{1}$ and $e_{2}$ be unit vectors, and the angle between $e_{1}$ and $e_{2}$ is $\frac{\pi}{3}$. If $a=e_{1}+3e_{2}$ and $b=2e_{1}$, then the projection of vector $a$ in the direction of $b$ is __________.

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