
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 \(a, b, c, d\) such that \(a \geqslant b\), \(c \geqslant d\), and \(|a| + 2|b| + 3|c| + 4|d| = 1\), define \(P = (a - b)(b - c)(c - d)\). Determine the minimum and maximum values of \(P\).

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