
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
Determine the smallest positive integer $x$ such that $x = \frac{p! \cdot q!}{r! \cdot s!} + \frac{u! \cdot v!}{w! \cdot t!}$ satisfies $x = 145$, where $p, q, r, s, u, v, w, t$ are positive integers. Additionally, ensure that $p + r$ and $u + w$ are as small as possible. What is $u + w$?
**A)** 5  
**B)** 6  
**C)** 7  
**D)** 8  
**E)** 9

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