
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  $F$ ,  $D$ , and  $E$  be points on the sides  $[AB]$ ,  $[BC]$ , and  $[CA]$  of  $\triangle ABC$ , respectively, such that  $\triangle DEF$  is an isosceles right triangle with  hypotenuse  $[EF]$ . The altitude of  $\triangle ABC$  passing through  $A$  is  $10$  cm. If  $|BC|=30$  cm, and  $EF \parallel BC$ , calculate the perimeter of  $\triangle DEF$ .

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