
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
A one-person game with two possible outcomes is played as follows:
After each play, the player receives either  $a$  or  $b$  points, where  $a$  and  $b$  are integers with  $0 < b < a < 1986$ . The game is played as many times as one wishes and the total score of the game is defined as the sum of points received after successive plays. It is observed that every integer  $x \geq 1986$  can be obtained as the total score whereas  $1985$  and  $663$  cannot. Determine  $a$  and  $b.$ 

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