
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 domain of the function \( f(x) \) is \(\mathbf{R}\) and it satisfies the following conditions: for \( x \in [0, 1) \), \( f(x) = 2^x - x \), and for any real number \( x \), \( f(x) + f(x+1) = 1 \). Let \( a = \log_2 3 \). Find the value of the expression \( f(a) + f(2a) + f(3a) \).

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