
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 a right triangle  $ABC$  ( $\angle C = 90^o$ ) it is known that  $AC = 4$  cm,  $BC = 3$  cm. The points  $A_1, B_1$  and  $C_1$  are such that  $AA_1 \parallel BC$ ,  $BB_1\parallel A_1C$ ,  $CC_1\parallel A_1B_1$ ,  $A_1B_1C_1= 90^o$ ,  $A_1B_1= 1$  cm. Find  $B_1C_1$ .

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