
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
Given distinct natural numbers \(a_{1}, a_{2}, \ldots, a_{14}\). All 196 numbers of the form \(a_{k}+a_{\ell}\), where \(1 \leqslant k, \ell \leqslant 14\), are written on the board. Is it possible that for any combination of two digits among the numbers written on the board, there exists at least one number ending in that combination (i.e., numbers ending in \(00, 01, 02, \ldots, 99)\)?

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