
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
Positive integers $a$, $b$, and $c$ are chosen so that $a<b<c$, and the system of equations \[
2x + y = 2023\quad\text{and}\quad y = |x-a| + |x-b| + |x-c|
\]has exactly one solution. Determine the minimum value of $c$.

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