
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 coordinate plane, there are two regions M and N. M is defined by the inequalities y ≥ 0, y ≤ x, and y ≤ 2 - x, and N is defined by the inequality t ≤ x ≤ t + 1, where 0 ≤ t ≤ 1. Let f(t) be the function representing the common area of M and N. Determine f(t).

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