
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 vectors $\overrightarrow{a}$, $\overrightarrow{b}$, and $\overrightarrow{c}$, it is known that $\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} = 0$. Also, the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $60^{\circ}$, and the magnitudes of $\overrightarrow{a}$ and $\overrightarrow{b}$ are $2$ and $4$, respectively. Determine the magnitude of $\overrightarrow{c} ($$\overrightarrow{c}$$)$.

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