
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
Rhombus $PQRS$ is inscribed in rectangle $ABCD$ such that vertices $P$, $Q$, $R$, and $S$ are on the rectangle's sides $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, and $\overline{DA}$, respectively. Given that $PB=10$, $BQ=25$, $PR=35$, and $QS=45$, calculate the perimeter of rectangle $ABCD$ and express your answer in the form $m+n$ where $m/n$ is the perimeter in lowest terms.

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