
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 real numbers a, b, and c satisfy the system of equations
\[
\left\{\begin{array}{l}
a^{2}-bc-8a+7=0 \\
b^{2}+c^{2}+bc-6a+6=0
\end{array}\right.
\]
determine the range of values for a.

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