
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 \(a\) and \(b\) be real numbers that satisfy the equations
\[
\frac{a}{b}+\frac{b}{a}=\frac{5}{2} \quad \text{and} \quad a-b=\frac{3}{2}.
\]
Find all possible values of \(a^{2}+2ab+b^{2}+2a^{2}b+2ab^{2}+a^{2}b^{2}\).

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