
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 quadratic equations in \( x \),
\[ x^{2} + kx - 12 = 0 \]
and
\[ 3x^{2} - 8x - 3k = 0, \]
having a common root, find all possible values of the real number \( k \).

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