
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
Eight distinct pieces of candy are to be distributed among four bags. The red bag and the blue bag must each receive at least one piece of candy; the white bag and green bag may remain empty. How many valid candy distributions are possible?
A) $895$
B) $1,023$
C) $1,535$
D) $\sum_{r=1}^{7} \binom{8}{r} (2^{8-r} - 1)$
E) $2,040$

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