
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
In the rectangular table shown below, the number  $1$  is written in the upper-left hand corner, and every number is the sum of the any numbers directly to its left and above.  The table extends infinitely downwards and to the right.
\[ 
  \begin{array}{cccccc}
    1 & 1 & 1 & 1 & 1 & \cdots 
    1 & 2 & 3 & 4 & 5 & \cdots 
    1 & 3 & 6 & 10 & 15 & \cdots 
    1 & 4 & 10 & 20 & 35 & \cdots 
    1 & 5 & 15 & 35 & 70 & \cdots 
    \vdots & \vdots & \vdots & \vdots & \vdots & \ddots
  \end{array}
\]
Wanda the Worm, who is on a diet after a feast two years ago, wants to eat  $n$  numbers (not necessarily distinct in value) from the table such that the sum of the numbers is less than one million. However, she cannot eat two numbers in the same row or column (or both). What is the largest possible value of  $n$ ?

*Proposed by Evan Chen*

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