
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
A gardener plants two maple trees, six oaks, and six birch trees in a row. The gardener wants at least one oak at each end of the row. In random order, with each arrangement equally likely, find the probability that no two birch trees are adjacent. Express your answer as $\frac{m}{n}$ in lowest terms and find $m+n$.

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