
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
A regular tetrahedron  $SABC$  of volume  $V$  is given. The midpoints  $D$  and  $E$  are taken on  $SA$  and  $SB$  respectively and the point  $F$  is taken on the edge  $SC$  such that  $SF: FC = 1: 3$ . Find the volume of the pentahedron  $FDEABC$ .

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