
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
A triangle has angles in arithmetic progression, and the side lengths are $5, 7, x$. If the smallest angle is $40^\circ$, find the sum of the possible values of $x$. Express your answer as $a + \sqrt{b} + \sqrt{c}$, where $a, b, c$ are positive integers.
A) $\sqrt{50}$
B) $\sqrt{60}$
C) $\sqrt{62}$
D) $\sqrt{70}$

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