
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 \(\left\{\begin{array}{c}10 x^{2}+x-a-11=0 \\ 4 x^{2}+(a+4) x-3 a-8=0\end{array} \right.\) consistent? Solve the system for all allowable \(a\).

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