
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
On a board there are written the integers from  $1$  to  $119$ . Two players,  $A$  and  $B$ , make a move by turn. A  $move$  consists in erasing  $9$  numbers from the board. The player after whose move two numbers remain on the board wins and his score is equal with the positive difference of the two remaining numbers. The player  $A$  makes the first move. Find the highest integer  $k$ , such that the player  $A$  can be sure that his score is not smaller than  $k$ .

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