
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
Source: 2017 Canadian Open Math Challenge, Problem A4
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Three positive integers  $a$ ,  $b$ ,  $c$  satisfy  $$ 4^a \cdot 5^b \cdot 6^c = 8^8 \cdot 9^9 \cdot 10^{10}. $$  Determine the sum of  $a + b + c$ .


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