
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
(1) Find the coefficient of $x^3$ in the expansion of $(\frac{1}{2} - x)^5$ and the sum of all coefficients in the expansion.
(2) From the numbers 0, 2, 3, 4, 5, 6, select any 4 to form a 4-digit number without repeating digits. Find the number of 4-digit numbers that meet the condition.

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