
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
If $a \equiv 24 \pmod{50}$ and $b \equiv 95 \pmod{50}$, then for what integer $n$ in the set $\{150, 151, 152, \ldots, 200\}$ is it true that $$a-b \equiv n \pmod{50}~?$$ Moreover, find $n$ such that it also satisfies $n \equiv 3 \pmod{4}$.

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