
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 five maple trees, three oak trees, and seven birch trees in a row. He plants them in random order with each arrangement being equally likely. What is the probability that no two birch trees are adjacent to each other and the row starts with a maple tree? Let $\frac{m}{n}$ in lowest terms represent this probability. Find $m+n$.

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