
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
The number 2027 is prime. For \( i=1,2, \ldots, 2026 \), let \( p_{i} \) be the smallest prime number such that \( p_{i} \equiv i \pmod{2027} \). Estimate \( \max \left(p_{1}, \ldots, p_{2026}\right) \). Submit a positive integer \( E \).

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