
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
Points $P, Q, R$, and $S$ are distinct and positioned consecutively on a straight line. The lengths of line segments $PQ, PR$, and $PS$ are $a, b$, and $c$ respectively. The segments $PQ$ and $RS$ can pivot around points $Q$ and $R$ in such a way that points $P$ and $S$ coincide to form a triangle with sides $\ell, m,$ and $n$. Given $b = a + c$, find the conditions under which a triangle with positive area can be formed.
A) $a > c$
B) $c > 2a$
C) $b > 3a$
D) $b < a$

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