
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 inequality regarding $x$, $\log_{2}(-2x^2 + 3x + t) < 0$, where $t \in \mathbb{R}$.
$(1)$ When $t=0$, find the solution to the inequality;
$(2)$ If there is a solution to the inequality, find the range of values for the real number $t$.

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