
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
If $x$ is a real number and $|x-5| + |x-3| + |x-2| < b$ where $b > 0$, find the range of $b$ such that the inequality holds for some $x$.
A) $0 < b \leq 4$  
B) $b > 4$  
C) $b = 4$  
D) $0 < b < 4$  
E) $b \geq 4$

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