
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 that the base of a triangle is $\left(2x+1\right)cm$ long and the height is $\left(x-2\right)cm$, if both the base and height are increased by $5$ centimeters, how much does the area of the triangle increase? Also, find the increase in area when $x=3$.

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