
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
Given that a set $T$ of points in the $xy$-plane is symmetric about the origin, both coordinate axes, and the line $y = x$, and that the point $(1,4)$ is in $T$, find the smallest number of points in $T$.

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