
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 $1,2,3,4,5,6$ where the first term cannot be $1$ or $2$ and the second term cannot be $3$. Find the probability that the third term is $4$, expressed in lowest terms, as $a/b$, and calculate $a+b$.

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