
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
Let \( p > 3 \) be a prime number. Determine the last two digits of the number

\[ \sum_{i=1}^{p} \binom{i \cdot p}{p} \cdot \binom{(p-i+1) p}{p} \]

in base \( p \).

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