
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$ ,  $ c$ , and  $ d$  satisfy  $ a > b > c > d$ ,  $ a \plus{} b \plus{} c \plus{} d \equal{} 2010$ , and  $ a^2 \minus{} b^2 \plus{} c^2 \minus{} d^2 \equal{} 2010$ . Find the number of possible values of  $ a$ .

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