
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
There are  $5$  vertices labelled  $1,2,3,4,5$ . For any two pairs of vertices  $u, v$ , the edge  $uv$ is drawn with probability  $1/2$ . If the probability that the resulting graph is a tree is given by  $\dfrac{p}{q}$  where  $p, q$  are coprime, then find the value of  $q^{1/10} + p$ .

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