
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
Let  $s_1, s_2, s_3$  be the three roots of  $x^3 + x^2 +\frac92x + 9$ .  $$ \prod_{i=1}^{3}(4s^4_i + 81) $$   can be written as  $2^a3^b5^c$ . Find  $a + b + c$ .

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