
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 straight line  $l_{1}$  with equation  $x-2y+10 = 0$  meets the circle with equation  $x^2 + y^2 = 100$  at B in the  first quadrant. A line through B, perpendicular to  $l_{1}$  cuts the y-axis at P (0, t). Determine the value of  $t$ .

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