
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 power function $f(x) = (k^2 + k - 1)x^{k^2 - 3k}$ ($k \in \mathbb{Z}$), its graph is symmetric about the y-axis and is a decreasing function on $(0, +\infty)$. The value of $k$ is \_\_\_\_\_\_.

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