
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
(1) Given that $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ are two unit vectors with an angle of $60^{\circ}$ between them, $\overrightarrow{a}=3 \overrightarrow{e_{1}}-2 \overrightarrow{e_{2}}$, and $\overrightarrow{b}=2 \overrightarrow{e_{1}}-3 \overrightarrow{e_{2}}$, find $\overrightarrow{a} \cdot \overrightarrow{b}$;
(2) Given $\overrightarrow{a}=(3,4)$ and $\overrightarrow{b}=(2,-1)$, find $\overrightarrow{a} \cdot \overrightarrow{b}$ and the projection of $\overrightarrow{a}$ on $\overrightarrow{b}$.

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