
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 $f(x)=k⋅a^{x}-a^{-x}$ where $a > 0$ and $a \neq 1$, and it is an odd function.

1. Find the value of the constant $k$.
2. Assuming $a > 1$, determine the monotonicity of the function $y=f(x)$ on $\mathbb{R}$, and solve the inequality $f(x^{2})+f(2x-1) < 0$ with respect to $x$.

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