
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
Suppose  $x$  is a random real number between  $1$  and  $4$ , and  $y$  is a random real number between  $1$  and  $9$ . If the expected value of \[ \left\lceil \log_2 x \right\rceil - \left\lfloor \log_3 y \right\rfloor \] can be expressed as  $\frac mn$  where  $m$  and  $n$  are relatively prime positive integers, compute  $100m + n$ .

*Proposed by Lewis Chen*

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