
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 $T$ be the set of permutations of the sequence $1, 2, 3, 4, 5, 6$ for which the first term is not $1$ or $6$. A permutation is chosen randomly from $T$. The probability that the third term is $3$, in lowest terms, is $p/q$. What is $p+q$?
A) 5
B) 6
C) 11
D) 16
E) 20

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