
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 that \( f(x) = \begin{cases} 
-2x + 1, & \text{when } x < 1 \\
x^2 - 2x, & \text{when } x \geq 1 
\end{cases} \). If \( d \) is the maximum integral solution of \( f(x) = 3 \), find the value of \( d \).

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