
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 the following conditions:①$\angle C=\angle A-\angle B$；②$\angle A:\angle B:\angle C=5:2:3$；③$a=\frac{3}{5}c$,$b=\frac{4}{5}c$；④$a:b:c=1:2$:$\sqrt{3}$, the number of conditions that can determine $\triangle ABC$ to be a right triangle is ______.

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