
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 vectors \\( \overset{→}{\alpha}, \overset{→}{\beta}, \overset{→}{c} \\) in the same plane satisfying \\( |\overset{→}{\alpha}| = |\overset{→}{\beta}| = 1 \\), the angle between vector \\( \overset{→}{\alpha} \\) and \\( \overset{→}{\beta} - \overset{→}{\alpha} \\) is \\(120^{\circ}\\), and \\(( \overset{→}{\alpha} - \overset{→}{c}) \cdot ( \overset{→}{\beta} - \overset{→}{c}) = 0 \\), then the range of \\( |\overset{→}{c}| \\) is.

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