
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
Find all values of the parameter $a$ for which the equation

$$
3 x^{2}-4(3 a-2) x+a^{2}+2 a=0
$$

has roots $x_{1}$ and $x_{2}$ that satisfy the condition $x_{1}<a<x_{2}$.

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