
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
 Let be  $f: (0,+\infty)\rightarrow \mathbb{R}$  monoton-decreasing . 

If  $f(2a^2+a+1)<f(3a^2-4a+1)$  find interval of  $a$  .


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