
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
Consider the configurations of integers $a_{1,1}$  $a_{2,1} \quad a_{2,2}$  $a_{3,1} \quad a_{3,2} \quad a_{3,3}$  $\dots \quad \dots \quad \dots$  $a_{2017,1} \quad a_{2017,2} \quad a_{2017,3} \quad \dots \quad a_{2017,2017}$ Where  $a_{i,j} = a_{i+1,j} + a_{i+1,j+1}$  for all  $i,j$  such that  $1 \leq j \leq i \leq 2016$ .
Determine the maximum amount of odd integers that such configuration can contain.

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