
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 two fixed points in the Cartesian coordinate system, \\(F_{1}(0,-2)\\) and \\(F_{2}(0,2)\\), and a moving point \\(M\\) in the plane such that the triangle \\(\\triangle MF_{1}F_{2}\\) satisfies the condition \\(\\sin \\angle MF_{1}F_{2} = \\sqrt{3}\\sin \\angle MF_{2}F_{1}\\), then the range of values for \\(\\overrightarrow{MF_{1}} \cdot \overrightarrow{MF_{2}}\\) is \_\_\_\_\_\_\_\_.

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