
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
Consider a polynomial
\[ b_6 x^6 + b_5 x^5 + b_4 x^4 + \dots + b_1 x + b_0 = 0 \]
with integer coefficients, where all roots \( s_1, s_2, \dots, s_6 \) are integers. Moreover, the roots of the polynomial
\[ b_0 x^6 + b_1 x^5 + b_2 x^4 + \dots + b_4 x^2 + b_5 x + b_6 = 0 \]
are also \( s_1, s_2, \dots, s_6 \). Determine the number of possible multisets \( T = \{s_1, s_2, \dots, s_6\} \).

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