
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
When studying the correlation between two variables, it is observed that the sample points in the scatter plot are concentrated around a certain exponential curve $y=e^{bx+a}$. Let $z=\ln y$, and the linear regression equation is obtained as $\hat{z} =0.25x-2.58$. Determine the regression equation for this model.

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