
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
If \( 208208 = 8^{5}a + 8^{4}b + 8^{3}c + 8^{2}d + 8e + f \), where \( a, b, c, d, e, \) and \( f \) are integers and \( 0 \leq a, b, c, d, e, f \leq 7 \), find the value of \( a \times b \times c + d \times e \times f \).

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