
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 real numbers $a$, $b$, $c$, and $b \neq 0$. If real numbers $x_1$, $x_2$, $y_1$, $y_2$ satisfy $x_1^2 + ax_2^2 = b$, $x_2y_1 - x_1y_2 = a$, $x_1y_1 + ax_2y_2 = c$, then the value of $y_1^2 + ay_2^2$ is.

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