
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
[b]Problem Section #2
a) If   $$ ax+by=7 $$     $$ ax^2+by^2=49 $$     $$ ax^3+by^3=133 $$     $$ ax^4+by^4=406 $$   , 
find the value of     $2014(x+y-xy)-100(a+b).$ 

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