
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
The solution fails if some inequalities turn into equalities. To fix the problems, it is sufficient to only replace some of the $\leqslant, \geqslant$ signs with $<$, $>$ or vice versa. Otherwise, the solution contains no other errors. - 6 points.

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