
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
Given that $\boldsymbol{a}$ and $\boldsymbol{b}$ are unit vectors and $|3 \boldsymbol{a} + 4 \boldsymbol{b}| = |4 \boldsymbol{a} - 3 \boldsymbol{b}|$, and that $|\boldsymbol{c}| = 2$, find the maximum value of $|\boldsymbol{a} + \boldsymbol{b} - \boldsymbol{c}|$.

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