
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 function $$y=b+a^{x^{2}+2x}$$ (where $a$ and $b$ are constants, $a>0$ and $a\neq1$) has a maximum value of 3 and a minimum value of $\frac{5}{2}$ in the interval $$\left[-\frac{3}{2}, 0\right]$$. Find the values of $a$ and $b$.

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