
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 function $f\left(x\right)=a^{x}-a^{-x}$ ($a \gt 0$, and $a\neq 1$), and $f(1)=\frac{3}{2}$.  
$(1)$ Find the value of $a$;  
$(2)$ If $f\left(2t\right)+f\left(t-1\right) \lt 0$, find the range of values for $t$.

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