
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
Suppose that $\triangle{DEF}$ is an equilateral triangle of side length $t$, and there is a unique point $Q$ inside the triangle such that $DQ = 2$, $EQ = 2\sqrt{2}$, and $FQ = 3$. Determine the value of the side length $t$.

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