
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
Some positive integers are initially written on a board, where each  $2$  of them are different.
Each time we can do the following moves:
(1) If there are 2 numbers (written in the board) in the form  $n, n+1$  we can erase them and write down  $n-2$ (2) If there are 2 numbers (written in the board) in the form  $n, n+4$  we can erase them and write down  $n-1$ After some moves, there might appear negative numbers. Find the maximum value of the integer  $c$  such that:
Independetly of the starting numbers, each number which appears in any move is greater or equal to  $c$ 

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