
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
Let $x$ be a real number and $|x-2| + |x-5| + |x-10| < b$ where $b > 0$. Find the range of $b$ where this inequality holds for some real number $x$.
A) $0 < b \leq 8$
B) $b > 8$
C) $0 < b < 8$
D) $b \geq 8$
E) $8 < b \leq 10$

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