
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
For any two points A$(x_1, y_1)$ and B$(x_2, y_2)$ in the Cartesian coordinate plane, define a kind of "distance" between them: $\|AB\| = |x_2 - x_1| + |y_2 - y_1|$. Consider the following three propositions:  
① If point C is on the line segment AB, then $\|AC\| + \|CB\| = \|AB\|$.  
② In $\triangle ABC$, if $\angle C = 90^\circ$, then $\|AC\|^2 + \|CB\|^2 = \|AB\|^2$.  
③ In $\triangle ABC$, $\|AC\| + \|CB\| > \|AB\|$.  
Among these, the true propositions are (write down all the codes of true propositions).

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