
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 the following conclusions:
1. $\overrightarrow{a} \cdot \overrightarrow{b} \in R$, while $(\overrightarrow{a} \cdot \overrightarrow{b}) \cdot \overrightarrow{c} \notin R$;
2. $\overrightarrow{AB} + \overrightarrow{BC} - \overrightarrow{AC} = 0$;
3. The projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ is $|\overrightarrow{b}| \cos \theta$, where $(\overrightarrow{a}, \overrightarrow{b}) = \theta$;
4. Given non-zero vectors $\overrightarrow{a}$, $\overrightarrow{b}$, $\overrightarrow{c}$, which are not pairwise collinear, if $(\overrightarrow{a} \cdot \overrightarrow{b}) \cdot \overrightarrow{c} = (\overrightarrow{b} \cdot \overrightarrow{c}) \cdot \overrightarrow{a}$, then $\overrightarrow{a}$ is parallel to $\overrightarrow{c}$.
Determine the correct answer(s) from the above conclusions.

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