
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
Let the real numbers \(a, b, c\) satisfy
\[
\begin{cases}
a^{2} - bc - 8a + 7 = 0 \\
b^{2} + c^{2} + bc - 6a + 6 = 0,
\end{cases}
\]

Find the range of values for \(a\).

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