
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 the angle between the unit vectors $e\_1$ and $e\_2$ is $\frac{2π}{3}$, $a=e\_1+2e\_2$, and $b=2e\_1-3e\_2$, find the projection of $b$ in the direction of $a$.

A) $-\frac{3\sqrt{3}}{2}$
B) $-\sqrt{3}$
C) $\sqrt{3}$
D) $\frac{3\sqrt{3}}{2}$

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