
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
45. a) What values can the following angles of triangle $ABC$ take if $A \leqslant B \leqslant C$?
1) Angle $A$;
2) Angle $B$;
3) Angle $C$.

b) The area of the triangle with sides $a, b,$ and $c$ where $a \leqslant b \leqslant c$ is equal to 1. What values can the following sides of the triangle take?
1) Side $a$;
2) Side $b$;
3) Side $c$.

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