
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 functions $f(x) = x^3 + 1$ and $g(x) = 2(\log_2{x})^2 - 2\log_2{x} + t - 4$, if the function $F(x) = f(g(x)) - 1$ has exactly two distinct zeros in the interval $[1, 2\sqrt{2}]$, determine the range of the real number $t$.

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