
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 real numbers $a$, $b$, $c$, $d$ satisfying the equations $\frac{a - 2e^a}{b} = \frac{1 - c}{d - 1} = 1$, where $e$ is the base of the natural logarithm, find the minimum value of $(a-c)^2 + (b-d)^2$.

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