
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  $p$  be a prime number.  $T(x)$  is a polynomial with integer coefficients and degree from the set  $\{0,1,...,p-1\}$  and such that  $T(n) \equiv T(m)  (mod p)$  for some integers m and n implies that  $ m \equiv n (mod p)$ . Determine the maximum possible value of degree of  $T(x)$ 

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