
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
The base of the pyramid \(SABC\) is an isosceles triangle \(ABC\) with \(AB = BC = 3\) and \(AC = 5\). The height of the pyramid \(SABC\) is the segment \(SO\), where \(O\) is the intersection point of the line passing through vertex \(B\) parallel to side \(AC\), and the line passing through \(C\) perpendicular to side \(AC\). Find the distance from the center of the inscribed circle of triangle \(ABC\) to the plane containing the lateral face \(BSC\), given that the height of the pyramid is \(7/12\).

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