
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
For which values of \(a\) is the system 
\[
\left\{\begin{array}{l}
12 x^{2}+48 x-a+36=0 \\
(a+60) x-3(a-20)=0
\end{array}\right.
\]
consistent? Solve the system for all permissible \(a\).

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