
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 has to plant three oaks, four holm oaks, and five beeches in a row along a path. The trees are planted randomly, with the probability of planting any particular tree being the same.

Find the probability that, once all the trees are planted, no two beeches are consecutive.

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