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

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