
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
Draw the triangle $ABC$ and an arbitrary line $PQ$. If the distances from the vertices $A$, $B$, and $C$ and the midpoints of the sides to the line $PQ$ are $a$, $b$, $c$, respectively, and $a_{1}$, $b_{1}$, $c_{1}$, respectively, then

$$
a + b + c = a_{1} + b_{1} + c_{1}
$$

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