
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 two quadratic functions $y_1$ and $y_2$, when $x=\alpha$ ($\alpha>0$), $y_1$ reaches its maximum value of 5, and $y_2=25$. Additionally, the minimum value of $y_2$ is -2, and $y_1+y_2=x^2+16x+13$. Find the value of $\alpha$ and the expressions for the quadratic functions $y_1$ and $y_2$.

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