
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
In a certain grade, competitions in mathematics, physics, and chemistry were held successively. The number of students who participated in at least one subject were: mathematics $203$ students, physics $179$ students, and chemistry $165$ students; those who participated in two subjects were: mathematics and physics $143$ students, mathematics and chemistry $116$ students, physics and chemistry $97$ students; and those who participated in all three subjects were $89$ students. Find the total number of students who participated in the competitions.

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