
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
Let the set 
\[ \left\{\left.\frac{3}{a}+b \right\rvert\, 1 \leqslant a \leqslant b \leqslant 4\right\} \]
have maximum and minimum elements denoted by \( M \) and \( N \) respectively. Find \( M - N \).

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