
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 semicircle with centre  $O$  and the diameter  $AC$  is divided in two arcs  $AB$  and  $BC$  with ratio  $1: 3$ .  $M$  is the midpoint of the radium  $OC$ . Let  $T$  be the point of arc  $BC$  such that the area of the cuadrylateral  $OBTM$  is maximum. Find such area in fuction of the radium.

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