
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
In a right-angled triangle $DEF$ ($\angle EDF$ is the right angle), a circle is inscribed so that it touches $DE$, $EF$, and $FD$ at points $A$, $B$, and $C$ respectively. If $EF$ is the hypotenuse having a length of 10 units, and $DE = 6$ units, find the length $x$ of $FD$.
A) 5
B) 6
C) 7
D) 8

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