
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 the roots of the equation $x^2 - mx + 3 = 0$. Suppose that $a^2 + \frac{1}{b^2}$ and $b^2 + \frac{1}{a^2}$ are the roots of the equation $x^2 - sx + t = 0$. Determine the value of $t$.

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