
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 $\overset{⇀}{a}=(1,-3), \overset{⇀}{b}=(-2,6)$, if the angle between vector $\overset{⇀}{c}$ and $\overset{⇀}{a}$ is $60^{\circ}$, and $\overset{⇀}{c}·( \overset{⇀}{a}+ \overset{⇀}{b})=-10$, find the magnitude of vector $\overset{⇀}{c}$, denoted as $|\overset{⇀}{c}|$.

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