
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 three non-zero vectors $\bar{a}, \bar{b}, \bar{c}$, each pair of which is non-collinear. Find their sum, if $(\bar{a}+\bar{b}) \| \bar{c}$ and $(\bar{b}+\bar{c}) \| \bar{a}$.

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