
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 vectors $\overrightarrow{a}$, $\overrightarrow{b}$, and $\overrightarrow{c}$ that are not coplanar and form equal angles between each pair. If $|\overrightarrow{a}|=1$, $|\overrightarrow{b}|=1$, and $|\overrightarrow{c}|=3$, find $|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|=\_\_\_\_\_\_\_\_$.

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