
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
Consider the function \( f(x)=(2k-1)a^{x}-a^{-x} \) where \( a > 0 \) and \( a \neq 1 \), and it's defined as an odd function over the domain \( \mathbb{R} \).
(1) Determine the value of \( k \);
(2) If \( f(1)=- \frac{5}{6} \), the inequality \( f(3x-t)+f(-2x+1) \geq 0 \) holds for all \( x \in [-1,1] \). Find the minimum value of the real number \( t \).

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