
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
Define a sequence of integers by  $T_1 = 2$  and for  $n\ge2$ ,  $T_n = 2^{T_{n-1}}$ . Find the remainder when  $T_1 + T_2 + \cdots + T_{256}$  is divided by 255.

*Ray Li.*

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