
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 n be a set of integers.  $S(n)$  is defined as the sum of the elements of n.  $T=\{1,2,3,4,5,6,7,8,9\}$  and A and B are subsets of T such that A  $\cup$   $B=T$  and A  $\cap$   $B=\varnothing$ . The probability that  $S(A)\geq4S(B)$  can be expressed as  $\frac{p}{q}$ . Compute  $p+q$ .

*2022 CCA Math Bonanza Team Round #8*

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