
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
Rectangle $ABCD$ contains a point $Q$ such that the distances from $Q$ to the vertices $A$, $B$, $C$, and $D$ are $5$, $x$, $13$, and $12$ inches respectively. Determine the value of $x$.
**A)** $5$  
**B)** $7$  
**C)** $5\sqrt{2}$  
**D)** $13$

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