
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
The coefficients of the polynomial
\[b_6 x^6 + b_5 x^5 + b_4 x^4 + b_3 x^3 + b_2 x^2 + b_1 x + b_0 = 0\]
are all integers, and its roots $s_1, s_2, \dots, s_6$ are all integers. Furthermore, the roots of the polynomial
\[b_0 x^6 + b_1 x^5 + b_2 x^4 + b_3 x^3 + b_4 x^2 + b_5 x + b_6 = 0\]
are also $s_1, s_2, \dots, s_6$. Find the number of possible multisets $T = \{s_1, s_2, \dots, s_6\}$ where the roots are restricted to ±1 and ±2.

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