
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 $T$ be a subset of $\{1,2,3,\ldots,1500\}$ such that no two members of $T$ differ by $5$ or $8$. What is the largest number of elements $T$ can have?

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