
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
In the right triangle \( \triangle ABC \), with \( \angle ACB = 90^\circ \), \( BC = a \), and \( CA = b \) (where \( a > 0 \) and \( b > 0 \)), point \( P \) lies on side \( AB \). The right triangle \( \triangle ABC \) is folded along line \( PC \) to form the tetrahedron \( PACB \). Find the maximum possible volume of this tetrahedron.

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