
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
Natural numbers \(a, b, c\) are chosen such that \(a < b < c\). It is also known that the system of equations \(2x + y = 2035\) and \(y = |x - a| + |x - b| + |x - c|\) has exactly one solution. Find the minimum possible value of \(c\).

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