
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 four maple trees, five oaks, and six birch trees in a row. He plants them in random order, each arrangement being equally likely. Calculate the probability that no two birch trees or no two maple trees are next to one another. Let this probability be $\frac{m}{n}$ in lowest terms and determine $m+n$.

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