
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 needs to plant three maple trees, four oak trees, and five birch trees in a row. He randomly determines the order in which these trees are planted, with all possible arrangements being equally likely. Let \(\frac{m}{n}\) represent the probability that no two birch trees are adjacent (expressed as a simplified fraction). Find \(m+n\).

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