
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
Below is the process of Little Le's calculation of square roots. Please read carefully and complete the corresponding tasks.

Calculate: $(\sqrt{3}+\sqrt{2})^{2}\times (5-2\sqrt{6})$.

Solution: Original expression $=(3+2\sqrt{6}+2)\times (5-2\sqrt{6})\ldots \ldots \ldots \ldots \ldots \ldots $ Step 1

$=(5+2\sqrt{6})\times (5-2\sqrt{6})\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $ Step 2

$=25-12\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $ Step 3

$=13.\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $ Step 4

Tasks:

(1) The mistake started in step ____ is due to ______.

(2) The correct result of the calculation is ______.

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