
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 equation $t^2 + 4at + 3a + 1 = 0$ (where $a > 1$) has two roots, both $tanα$ and $tanβ$, with $α, β \in \left( -\frac{π}{2}, \frac{π}{2} \right)$ and $x = α + β$,
1. Find the value of $tanx$;
2. Find the value of $\frac{cos2x}{\sqrt{2}cos\left(\frac{π}{4} + x\right)sinx}$.

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