
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 lattice point in the plane is a point of the form \((n, m)\), where \(n\) and \(m\) are integers. Consider a set \(S\) of lattice points. We construct the transform of \(S\), denoted by \(S^{\prime}\), by the following rule: the pair \((n, m)\) is in \(S^{\prime}\) if and only if any of \((n, m-1)\), \((n, m+1)\), \((n-1, m)\), \((n+1, m)\), or \((n, m)\) is in \(S\). How many elements are in the set obtained by successively transforming \(\{(0,0)\}\) 14 times?

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